The pair were meant to fight for Parker's World Boxing Organisation crown last month, but Englishman Fury pulled out citing a back injury.
Fury was replaced by Romanian Razvan Cojanu, who Parker beat in Auckland last month.
Now Duco Boss David Higgins told Radio LIVE's Sunday Sport an announcement will be made shortly about Parker and Fury getting in the ring together.
"The World Boxing Organisation has ordered we fight the mandatory challenger, which is Hughie Fury," Higgins said on RadioLive. "They had given us 30 days to negotiate terms with the Fury camp.